Firstly, congrats on your son using the potty! Isn't it exciting when they reach these big milestones?
Accidents will happen! So when you leave the house try to remember to remember to bring an extra pair of pants, underwear and socks and shoes maybe even. Plastic bag is handy to carry the soiled clothing articles. If you're outdoors, having wipes on hand is also useful. It's good to remind them all the time to use the potty, say 15 min's after eating/drinking or before sleeping. Often they would rather be playing rather than sitting on a potty!
As for the childcare, I'd discuss with the caretakers what there preference is and discuss an approach. Maybe you still want some reserve diapers there for during the naptimes (if he still naps). Personally I'd just go for it and send him in his underwear! Don't go backwards. That is what we did and it went fine. Sure, there are (still) accidents, so have to make sure there are extra underwear, pants, socks there on hand when this happens.
At their aunt's, I'd so the same, but maybe also supply her with some protection for the bed.
Good luck and hope this helps, from a mother of a girl (2.5) and boy (9 months)